Difference between revisions of "GeoGebra-5.04/C2/Properties-of-Quadrilaterals/English-timed"
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Latest revision as of 14:17, 24 September 2019
| Time | Narration |
| 00:01 | Welcome to this tutorial on Properties of Quadrilaterals in GeoGebra. |
| 00:07 | In this tutorial we will learn,
To construct quadrilaterals and understand the properties of quadrilaterals using GeoGebra. |
| 00:19 | Here I am using:
Ubuntu Linux OS, version 14.04 GeoGebra version 5.0.438.0-d |
| 00:31 | To follow this tutorial, learner should be familiar with GeoGebra interface. |
| 00:38 | If not for relevant GeoGebra tutorials, please visit our website. |
| 00:44 | Let us begin our demonstration. |
| 00:47 | I have already opened the GeoGebra interface. |
| 00:51 | For this tutorial, I will first uncheck the Axes. |
| 00:55 | To do that, right-click on Graphics view.
The Graphics menu opens. |
| 01:01 | Click on the Axes check-box. |
| 01:04 | I will increase the font size for better view. |
| 01:08 | Go to Options menu, navigate to Font Size. |
| 01:13 | From the sub-menu, select 18 pt radio button. |
| 01:17 | Now let us construct a parallelogram. |
| 01:20 | Click on the Segment with Given Length tool. |
| 01:24 | Click on the Graphics view. |
| 01:27 | The Segment with Given Length text box opens. |
| 01:31 | In the Length field, type 5 and click on OK button. |
| 01:37 | Segment AB with length 5 cm and labelled as f, is drawn. |
| 01:44 | Let us delete the point that was drawn mistakenly. |
| 01:48 | This point may not be required for the actual drawing. |
| 01:52 | Right-click on the point. From the sub-menu, select the Delete option. |
| 01:59 | Next click on the Parallel Line tool. |
| 02:02 | Click below line AB to draw point C then click on line AB. |
| 02:09 | A parallel line to segment AB passing through C, is drawn. |
| 02:14 | Using Segment tool, join the points A and C. |
| 02:21 | Click again on Parallel Line tool, click on segment AC and then click on point B. |
| 02:31 | Two parallel lines g and i intersect at a point. |
| 02:36 | Click on Intersect tool and click on the point of intersection as D. |
| 02:43 | Now using the Segment tool, join the points, C, D and D, B. |
| 02:53 | Parallelogram ABDC is now complete. |
| 02:57 | We will hide the lines g and i, so that we can see the parallelogram clearly. |
| 03:04 | Right-click on line g, from the submenu click on Show Object check-box.
Similarly I will hide the line i. |
| 03:15 | Now we will explore the properties of parallelogram ABDC. |
| 03:20 | From the Algebra view, we can find that,
segments f and j are equal and segments h and k are equal. |
| 03:31 | Observe that, the opposite sides are parallel and equal. |
| 03:36 | Let us now measure the angles of the parallelogram. |
| 03:40 | Click on Angle tool.
Click on the points D C A |
| 03:50 | C A B |
| 03:55 | A B D |
| 04:01 | B D C. |
| 04:07 | Observe that the opposite angles are equal. |
| 04:11 | Now we will convert the parallelogram ABDC to a rectangle. |
| 04:16 | Click on Move tool.
Click and drag point C until you see 90 degrees angle. |
| 04:25 | Drag the labels to see them clearly. |
| 04:30 | Observe that all the angles changed to 90 degrees. |
| 04:34 | Now let us learn to construct a kite. |
| 04:37 | For this I will open a new GeoGebra window. |
| 04:41 | Click on File and select New Window. |
| 04:46 | To contruct a kite, we will draw two circles that intersect at two points. |
| 04:52 | Click on Circle with Centre through point tool. |
| 04:55 | Then click on Graphics view. |
| 04:58 | Point A is drawn, this is the centre of the circle. |
| 05:03 | Click again at some distance from point A. |
| 05:07 | Point B appears.
This completes the circle c. |
| 05:13 | Similarly, we will draw another circle with centre C and passing through D. |
| 05:21 | Notice that the two circles c and d intersect at two points. |
| 05:26 | Click on Intersect tool and click on the circles c and d. |
| 05:33 | E and F are the intersection points of the circles. |
| 05:37 | Now let us draw the required quadrilateral using these circles. |
| 05:42 | Click on Polygon tool. |
| 05:44 | Click on the points A, E, C, F and A again to complete the quadrilateral. |
| 05:57 | Notice in the Algebra View that two pairs of adjacent sides are equal.
The drawn quadrilateral is a kite. |
| 06:06 | Pause the tutorial and do this assignment. |
| 06:10 | Measure the angles of the kite and check what happens. |
| 06:14 | Draw diagonals and locate the intersection point of the diagonals. |
| 06:19 | Measure the angle at the intersection of the diagonals. |
| 06:23 | Check if diagonals bisect each other. |
| 06:27 | Your completed assignment should look like this. |
| 06:32 | To delete all the objects, press Ctrl + A and then press Delete key on the Key board. |
| 06:40 | Now let us construct a rhombus. |
| 06:43 | Click on Segment with Given Length tool.
Click on the Graphics view. |
| 06:49 | Segment with Given Length text box opens. |
| 06:53 | In the Length field, type 4 and click on OK button.
A segment with 4 units is drawn. |
| 07:03 | Let us construct a circle with center A and passing through B. |
| 07:08 | Click on Circle with Centre through Point tool. |
| 07:11 | Click on points A and B to complete the circle. |
| 07:17 | Using Point tool, mark a point C on the circumference of the circle. |
| 07:23 | Click on Segment tool and then click on points A and C. |
| 07:29 | This will join the points A and C. |
| 07:32 | Click on the Parallel line tool and click on the line AB and then on point C. |
| 07:41 | We see a line parallel to AB passing through C. |
| 07:46 | Similarly, draw a parallel line to segment AC passing through B. |
| 07:53 | Notice that the lines i and h intersect at a point. |
| 07:58 | Using Intersect tool, we will mark the point of intersection as D. |
| 08:05 | Using the Segment tool, join the points A, D and B, C. |
| 08:13 | A quadrilateral ABDC with diagonals AD and BC is drawn. |
| 08:19 | The diagonals intersect at a point.
Using Intersect tool, mark the point of intersection as E. |
| 08:30 | Pause the tutorial and do this assignment. |
| 08:34 | Check if the diagonals of the quadrilateral ABDC bisect each other. |
| 08:40 | Also check if the diagonals are perpendicular bisectors. |
| 08:45 | Your completed assignment should look like this. |
| 08:49 | Now let us construct a cyclic quadrilateral. |
| 08:53 | For this, let us open Graphics 2 view. |
| 08:57 | Go to View menu and select Graphics 2 check box. |
| 09:03 | Graphics 2 view window opens, next to existing Graphics view. |
| 09:08 | Drag the border of the existing Graphics view, to see Graphics 2 view. |
| 09:13 | Now select Regular Polygon tool.
Click twice on Graphics 2 view. |
| 09:20 | The Regular Polygon text box opens with default value 4. |
| 09:25 | Click on the OK button. |
| 09:28 | A square FGHI is drawn in Graphics 2 view. |
| 09:33 | Let's construct perpendicular bisectors to segments FG and GH. |
| 09:39 | Select the Perpendicular Bisector tool from the tool bar. |
| 09:43 | Click on the points F, Gand G, H. |
| 09:50 | Observe that the perpendicular bisectors intersect at a point. |
| 09:55 | Using Intersect tool we will mark this point as J. |
| 10:01 | Now, Let's construct a circle with centre as J and passing through F. |
| 10:07 | Click on the Circle with center through Point tool, click on point J.
Then click on point F. |
| 10:16 | A cyclic quadrilateral FGHI is drawn. |
| 10:21 | Now we will display its area. |
| 10:24 | From the Angle tool drop down, click on the Area tool. |
| 10:28 | Then click on the quadrilateral FGHI to display its area. |
| 10:35 | As an assignment,
Draw a trapezium |
| 10:40 | Measure its perimeter and area. |
| 10:44 | Your completed assignment should look like this. |
| 10:49 | Let us summarise what we have learnt. |
| 10:52 | In this tutorial we have learnt, To construct quadrilaterals and understand the properties of quadrilaterals using GeoGebra. |
| 11:03 | The video at the following link summarises the Spoken Tutorial project.
Please download and watch it. |
| 11:11 | The Spoken Tutorial Project team conducts workshops using spoken tutorials and gives certificates.
For more details, please write to us. |
| 11:21 | Please post your questions in this forum. |
| 11:25 | Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
More information on this mission is available at this link. |
| 11:36 | This is Madhuri Ganapathi from, IIT Bombay signing off.
Thank you for watching. |
